$1.(8$ points$)$ Regular tires are made on one production line, and the other types of tires are made on a separate line. On the regular tire production line, the bottleneck resource can produce $480$ pallets of tires per week without failures. It fails on average every $84$ hours, and it has an average time to repair of $6$ hours.

a$.$ What is the minimum number of servers needed at the bottleneck station to keep utilization under $95\%$ on average?

b$.$ Assume interarrival CV is $0\mathrm{.}3,$ natural process time CV is $0\mathrm{.}3,$ and repair time CV is $1\mathrm{.}2.$ Given the number of servers, what are long$-$run cycle time, throughput and WIP?